Consider an experiment where an intervention X was manipulated and the behavioral outcome Y observed. After observing the outcome, a post-experimental questionnaire asked respondents about their attitudes towards the intervention, variable M. I want to test whether M is a mediator of X on Y. Given the impossibility to test for causation (since M was not manipulated externally) and especially given the criticisms of Bullock et al. 2010. Yes, but what's the mechanism? (don't expect an easy answer). doi: doi.org/10.1037/a0018933), does it make sense to go for this test? My primary interest is whether subjects that respond to X strongly are also those that perceive it in a certain way. Is a mediation analysis the right way to go here?
Regression analysis would answer this question in a simple way. But I can attach our mediation analyses so they can give you an idea:
If you're talking about mediation in the traditional sense, this assumes that the "attitude" variable M is influenced by X, and that M in turn has a causal effect on Y. In this case you can use mediation analysis, either with classic regression methods (eg Baron and Kenny) or structural equation modeling.
However your description sounds more like a case where M is fixed, but the effectiveness of intervention X depends on the value of M. This is a non-linear interaction, but you can easily assess it using interaction terms in a linear regression model.
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